PROGRAM f08qufe ! F08QUF Example Program Text ! Mark 23 Release. NAG Copyright 2011. ! .. Use Statements .. USE nag_library, ONLY : nag_wp, x04dbf, zgemm, ztrsen ! .. Implicit None Statement .. IMPLICIT NONE ! .. Parameters .. INTEGER, PARAMETER :: nin = 5, nout = 6 ! .. Local Scalars .. COMPLEX (KIND=nag_wp) :: alpha, beta REAL (KIND=nag_wp) :: s, sep INTEGER :: i, ifail, info, lda, ldc, ldq, ldt, & lwork, m, n ! .. Local Arrays .. COMPLEX (KIND=nag_wp), ALLOCATABLE :: a(:,:), c(:,:), q(:,:), t(:,:), & w(:), work(:) LOGICAL, ALLOCATABLE :: select(:) CHARACTER (1) :: clabs(1), rlabs(1) ! .. Intrinsic Functions .. INTRINSIC cmplx ! .. Executable Statements .. WRITE (nout,*) 'F08QUF Example Program Results' WRITE (nout,*) FLUSH (nout) ! Skip heading in data file READ (nin,*) READ (nin,*) n ldc = n lda = n ldq = n ldt = n lwork = (n*n)/2 ALLOCATE (a(lda,n),c(ldc,n),q(ldq,n),t(ldt,n),w(n),work(lwork), & select(n)) ! Read T, Q and the logical array SELECT from data file READ (nin,*) (t(i,1:n),i=1,n) READ (nin,*) READ (nin,*) (q(i,1:n),i=1,n) READ (nin,*) READ (nin,*) select(1:n) ! Compute Q * T * Q**T to find A alpha = cmplx(1,kind=nag_wp) beta = cmplx(0,kind=nag_wp) CALL zgemm('N','N',n,n,n,alpha,q,ldq,t,ldt,beta,c,ldc) CALL zgemm('N','C',n,n,n,alpha,c,ldc,q,ldq,beta,a,lda) ! Print Matrix A, as computed from Q * T * Q**T ! ifail: behaviour on error exit ! =0 for hard exit, =1 for quiet-soft, =-1 for noisy-soft ifail = 0 CALL x04dbf('General',' ',n,n,a,lda,'Bracketed','F7.4', & 'Matrix A created from Q*T*Q^T','Integer',rlabs,'Integer',clabs,80, & 0,ifail) WRITE (nout,*) FLUSH (nout) ! Reorder the Schur factor T and update the matrix Q to obtain TT and QT ! The NAG name equivalent of ztrsen is f08quf CALL ztrsen('Both','Vectors',select,n,t,ldt,q,ldq,w,m,s,sep,work,lwork, & info) ! Compute QT * TT * QT**T to find A alpha = cmplx(1,kind=nag_wp) beta = cmplx(0,kind=nag_wp) CALL zgemm('N','N',n,n,n,alpha,q,ldq,t,ldt,beta,c,ldc) CALL zgemm('N','C',n,n,n,alpha,c,ldc,q,ldq,beta,a,lda) ! Print Matrix A, as computed from QT * TT * QT**T ifail = 0 CALL x04dbf('General',' ',n,n,a,lda,'Bracketed','F7.4', & 'Matrix A created from QT*TT*QT^T','Integer',rlabs,'Integer',clabs, & 80,0,ifail) ! Print condition estimates WRITE (nout,*) WRITE (nout,99999) 'Condition number estimate', & ' of the selected cluster of eigenvalues = ', 1.0E0_nag_wp/s WRITE (nout,*) WRITE (nout,99999) 'Condition number estimate of the spec', & 'ified invariant subspace = ', 1.0E0_nag_wp/sep 99999 FORMAT (1X,A,A,1P,E10.2) END PROGRAM f08qufe